{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:22:51Z","timestamp":1758709371855},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2015,2,15]],"date-time":"2015-02-15T00:00:00Z","timestamp":1423958400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s11590-015-0860-0","type":"journal-article","created":{"date-parts":[[2015,2,17]],"date-time":"2015-02-17T10:48:35Z","timestamp":1424170115000},"page":"1763-1779","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Canonical duality for solving general nonconvex constrained problems"],"prefix":"10.1007","volume":"10","author":[{"given":"Vittorio","family":"Latorre","sequence":"first","affiliation":[]},{"given":"David Yang","family":"Gao","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,2,15]]},"reference":[{"key":"860_CR1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10589-005-1066-7","volume":"31","author":"EG Birgin","year":"2005","unstructured":"Birgin, E.G., Castillo, R.A., Martnez, J.M.: Numerical comparison of augmented Lagrangian algorithms for nonconvex problems. Comput. Optim. Appl. 31, 31\u201355 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"860_CR2","unstructured":"Chen, Y., Gao, D.Y. : Global solutions to large-scale spherical constrained quadratic minimization via canonical dual approach, to appear in Math Mech Solids (2014)"},{"key":"860_CR3","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611972597","volume-title":"Linear and nonlinear functional analysis with applications","author":"PG Ciarlet","year":"2013","unstructured":"Ciarlet, P.G.: Linear and nonlinear functional analysis with applications. SIAM, Philadelphia (2013)"},{"key":"860_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3176-7","volume-title":"Duality principles in nonconvex system: theory, methods and applications","author":"DY Gao","year":"2000","unstructured":"Gao, D.Y.: Duality principles in nonconvex system: theory, methods and applications. Kluwer Academic Publishers, Dordrecht (2000)"},{"key":"860_CR5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1023\/A:1026537630859","volume":"17","author":"DY Gao","year":"2000","unstructured":"Gao, D.Y.: Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. J. Glob. Optim. 17, 127\u2013160 (2000)","journal-title":"J. Glob. Optim."},{"key":"860_CR6","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1080\/02331930310001611501","volume":"52","author":"DY Gao","year":"2003","unstructured":"Gao, D.Y.: Perfect duality theory and complete set of solutions to a class of global optimization problems. Optimization 52, 467\u2013493 (2003)","journal-title":"Optimization"},{"key":"860_CR7","doi-asserted-by":"crossref","unstructured":"Gao, D.Y.: Nonconvex semi-linear problems and canonical duality solutions, in Advances in Mechanics and Mathematics II. In: Gao, D.Y., Ogden R.W. (eds.), pp. 261\u2013311. Kluwer Academic Publishers (2003)","DOI":"10.1007\/978-1-4613-0247-6_5"},{"key":"860_CR8","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1016\/j.compchemeng.2009.06.009","volume":"33","author":"DY Gao","year":"2009","unstructured":"Gao, D.Y.: Canonical duality theory: theory, method, and applications in global optimization. Comput. Chem. 33, 1964\u20131972 (2009)","journal-title":"Comput. Chem."},{"key":"860_CR9","unstructured":"Gao, D.Y.: Canonical duality-triality: Unified understanding bifurcation, chaos, and NP-hard problems in complexsystems. To appear in Int. J. Bifurcation Chaos"},{"key":"860_CR10","unstructured":"Gao, D.Y., Latorre, V., Ruan, N.: Advances in canonical duality theory, Volume I and II: special issues of Mathematics Mechanics Solids (2015)"},{"key":"860_CR11","unstructured":"Gao, D.Y., Ruan, N., Latorre, V.: Canonical duality-triality: Bridge between nonconvex analysis\/mechanics and global optimization in complex systems. In: Advances in canonical duality theory. special issues of Mathematics Mechanics Solids arxiv.org\/pdf\/1410.2665v2.pdf (2014)"},{"key":"860_CR12","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s10898-009-9399-x","volume":"45","author":"DY Gao","year":"2009","unstructured":"Gao, D.Y., Ruan, N., Sherali, H.D.: Solutions and optimality criteria for nonconvex constrained global optimization problems. J. Glob. Optim. 45, 473\u2013497 (2009)","journal-title":"J. Glob. Optim."},{"key":"860_CR13","doi-asserted-by":"crossref","unstructured":"Gao, D.Y., Sherali, H.D.: Canonical duality: Connection between nonconvex mechanics and global optimization. In: Advances in Application Mathematics and Global Optimization. pp 249\u2013316. Springer (2009)","DOI":"10.1007\/978-0-387-75714-8_8"},{"key":"860_CR14","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1090\/qam\/1012271","volume":"47","author":"DY Gao","year":"1989","unstructured":"Gao, D.Y., Strang, G.: Geometric nonlinearity: potential energy, complementary energy, and the gap function. Quart. Appl. Math. 47, 487\u2013504 (1989)","journal-title":"Quart. Appl. Math."},{"issue":"1","key":"860_CR15","doi-asserted-by":"crossref","first-page":"229","DOI":"10.3934\/jimo.2012.8.229","volume":"8","author":"DY Gao","year":"2012","unstructured":"Gao, D.Y., Wu, C.Z.: On the triality theory for a quartic polynomial optimization problem. J. Ind. Manag. Optim. 8(1), 229\u2013242 (2012)","journal-title":"J. Ind. Manag. Optim."},{"key":"860_CR16","unstructured":"Gao, D.Y., Wu, C.: On the triality theory in global optimization, preprint available at, http:\/\/arxiv.org\/abs\/1104.2970 (2011)"},{"key":"860_CR17","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1080\/02331930802355309","volume":"57","author":"DY Gao","year":"2008","unstructured":"Gao, D.Y., Yang, W.C.: Minimal distance between two non-convex surfaces. Optimization 57, 705\u2013714 (2008)","journal-title":"Optimization"},{"key":"860_CR18","doi-asserted-by":"publisher","unstructured":"Gao, T.K.: Complete solutions to a class of eighth-order polynomial optimization problems. IMA J. Appl. Math (2013). doi: 10.1093\/imamat\/hxt033","DOI":"10.1093\/imamat\/hxt033"},{"key":"860_CR19","unstructured":"Glowinski, R.: Augmented Lagrangian Methods: applications to the numerical solution of boundary-value problems, Elsevier Science (2000)"},{"key":"860_CR20","doi-asserted-by":"crossref","unstructured":"Lagrange, J.L.: Mecanique analytique. Courcier (1811), reissued by Cambridge University Press, 2009","DOI":"10.1017\/CBO9780511701788"},{"key":"860_CR21","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.neucom.2013.06.050","volume":"134","author":"V Latorre","year":"2013","unstructured":"Latorre, V., Gao, D.Y.: Canonical dual solution to nonconvex radial basis neural network optimization problem. Neurocomputing 134, 189\u2013197 (2013)","journal-title":"Neurocomputing"},{"key":"860_CR22","unstructured":"Marsden, J.E., Hughes, T.J.R.: Mathematical foundations of elasticity, Prentice-Hall (1983)"},{"key":"860_CR23","unstructured":"Morales-Silva, D., Gao, D.Y.: On the minimal distance between two surfaces, http:\/\/arxiv.org\/abs\/1210.1618 (2012)"},{"key":"860_CR24","unstructured":"Nocedal, J., Wright, S. J.: Numerical optimization (2nd edition). Springer (2006)"},{"key":"860_CR25","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1080\/10556788.2013.822497","volume":"29","author":"MJD Powell","year":"2013","unstructured":"Powell, M.J.D.: The Lagrange method and SAO with bounds on the dual variables. Optim. Methods. Softw. 29, 224\u2013238 (2013)","journal-title":"Optim. Methods. Softw."},{"key":"860_CR26","first-page":"116","volume":"75\u201376","author":"N Ruan","year":"2014","unstructured":"Ruan, N., Gao, D.Y.: Global optimal solutions to a general sensor network localization problem. Perform. Eval. 75\u201376, 116 (2014)","journal-title":"Perform. Eval."},{"key":"860_CR27","doi-asserted-by":"crossref","unstructured":"Tr\u00f6ltzsch, A.: A sequential quadratic programming algorithm for equality-constrained optimization without derivatives, Optim. Lett. (2014)","DOI":"10.1007\/s11590-014-0830-y"},{"key":"860_CR28","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1080\/00036811.2010.483427","volume":"90","author":"MD Voisei","year":"2010","unstructured":"Voisei, M.D., Zalinescu, C.: Some remarks concerning Gao-Strang\u2019s complementary gap function. Appl. Anal. 90, 1111\u20131121 (2010)","journal-title":"Appl. Anal."},{"key":"860_CR29","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s10898-010-9592-y","volume":"49","author":"MD Voisei","year":"2011","unstructured":"Voisei, M.D., Zalinescu, C.: Counterexamples to some triality and tri-duality results. J. Glob. Optim. 49, 173\u2013183 (2011)","journal-title":"J. Glob. Optim."},{"key":"860_CR30","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s10898-012-9881-8","volume":"54","author":"ZB Wang","year":"2012","unstructured":"Wang, Z.B., Fang, S.C., Gao, D.Y., Xing, W.X.: Canonical dual approach to solving the maximum cut problem. J. Glob. Optim. 54, 341\u2013352 (2012)","journal-title":"J. Glob. Optim."},{"key":"860_CR31","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.jtbi.2011.06.024","volume":"284","author":"J Zhang","year":"2011","unstructured":"Zhang, J., Gao, D.Y., Yearwood, J.: A novel canonical dual computational approach for prion AGAAAAGA amyloid fibril molecular modeling. J. Theor. Biol. 284, 149\u2013157 (2011)","journal-title":"J. Theor. Biol."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-015-0860-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-015-0860-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-015-0860-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-015-0860-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,6]],"date-time":"2023-08-06T02:02:17Z","timestamp":1691287337000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-015-0860-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,15]]},"references-count":31,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["860"],"URL":"https:\/\/doi.org\/10.1007\/s11590-015-0860-0","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,15]]}}}